What is the difference between vanilla policy gradient and advantage actor-critic?
The difference between Vanilla Policy Gradient (VPG) with a baseline as Value function and Advantage Actor Critic (A2C) is very similar to the difference between Monte Carlo Control and SARSA:

The value estimates used in updates for VPG are based on full sampled returns, calculated at the end of episodes.

The value estimates used in updates for A2C are based on temporal difference bootstrapped from e.g. a single step difference, and the Bellman function.


This leads to following practical differences:

A2C can learn during an episode which can lead to faster refinements in policy than with VPG.

A2C can learn in continuing environments, whilst VPG cannot.

A2C relies on initially biased value estimates, so can take more tuning to find hyperparameters for the agent that allow for stable learning. Whilst VPG typically has higher variance and can require more samples to achieve the same degree of learning.